Question 1

Read the following statements carefully and answer the question.

Statements:
1. A > B
2. B ≥ C
3. C > D
4. D = E
5. E < F

Which of the following conclusions is definitely TRUE based on the statements above?

Accepted Answer

Step 1: From statement 1, A > B. Step 2: From statement 2, B ≥ C, which means B is greater than or equal to C. Step 3: From statement 3, C > D. Step 4: From statement 4, D = E, so D and E are equal. Step 5: From statement 5, E < F, which means E is less than F. Now let us chain these relationships: - A > B (given) - B ≥ C (given) - C > D (given) - D = E (given) - E < F (given) Combining: A > B ≥ C > D = E < F From this chain: - A > C? Yes, because A > B and B ≥ C, so A > C is definitely true. - A > D? Yes, because A > B ≥ C > D, so A > D is definitely true. - A > E? Yes, because A > B ≥ C > D = E, so A > E is definitely true. - A > F? Cannot determine. We know A > E and E < F, but F could be greater than, equal to, or less than A. - B > D? Yes, because B ≥ C > D, so B > D is definitely true. - C > E? Yes, because C > D = E, so C > E is definitely true. Looking at the options, the conclusion that is definitely TRUE is: A > E.

Question 2

Given the following relationships:

A > B ≥ C
D < C ≤ E
F = B
E > A

Which of the following conclusions is definitely TRUE?

Accepted Answer

Step 1: List all given inequalities: - A > B ≥ C (so A > B, B ≥ C) - D < C ≤ E (so D < C, C ≤ E) - F = B - E > A Step 2: Chain the relationships: From A > B and B ≥ C, we get A > C. From C ≤ E and E > A, we get E > A > C, so E > C. From D < C and C ≤ E, we get D < E. Since F = B and A > B, we have A > F. Step 3: Evaluate each option: (a) D > C: We know D < C from the given. This is FALSE. (b) E > B: From E > A and A > B, we get E > B by transitivity. This is TRUE. (c) F > C: We know F = B and B ≥ C. This means F ≥ C, not strictly F > C. The relationship could be F = C. This is INDETERMINATE. (d) A = E: We know E > A from the given. This is FALSE. Therefore, answer is B.

Question 3

Study the following statements and answer the question:

Given:
1. A > B ≥ C
2. D < C ≤ E
3. F ≥ E > A

Which of the following conclusions is definitely TRUE?

A) F > B
B) D > B
C) C = E
D) A ≥ D

Accepted Answer

Let us analyze the given relationships step by step: From Statement 1: A > B ≥ C - This means: A is greater than B, and B is greater than or equal to C From Statement 2: D < C ≤ E - This means: D is less than C, and C is less than or equal to E From Statement 3: F ≥ E > A - This means: F is greater than or equal to E, and E is greater than A Now let's check each conclusion: **Option A: F > B (DEFINITELY TRUE)** Chain: F ≥ E > A > B - From Statement 3: F ≥ E and E > A - From Statement 1: A > B - Therefore: F ≥ E > A > B, which gives us F > B - This is definitely true. **Option B: D > B (INDETERMINATE)** - From Statement 1: B ≥ C - From Statement 2: D < C - So: D < C and B ≥ C, but we cannot determine if D > B or D ≤ B - Example: If B = 5, C = 5, D = 3, then D < B. If B = 5, C = 5, D = 4.5, then D < B. - This cannot be concluded. **Option C: C = E (FALSE)** - Statement 2 says: C ≤ E - This means C is less than or equal to E, but not necessarily equal - C could be less than E - This is not definitely true. **Option D: A ≥ D (INDETERMINATE)** - We know: A > B ≥ C and D < C - So: A > B ≥ C > D, giving us A > D - Wait, let me recheck: D < C means D is strictly less than C - And C ≤ B and B < A - Therefore: A > B ≥ C > D, so A > D (which also means A ≥ D) - However, let's verify with the other direction through E and F - A is not directly compared with D in a way that makes A ≥ D indeterminate - Actually: from D < C ≤ E > A, we cannot establish a direct relationship - Wait: E > A and D < C ≤ E, so we have D < C ≤ E and E > A, but this doesn't tell us about A vs D - This is indeterminate. **Correction to Option D verification:** Actually, let's be precise: D < C and C ≤ E and E > A, but A > B ≥ C So: A > B ≥ C > D, therefore A > D, which means A ≥ D is true. But the question asks what is DEFINITELY true, and Option A (F > B) is more clearly and directly true from the chain: F ≥ E > A > B. The answer is **A: F > B**

Question 4

Given the following relationships between six variables A, B, C, D, E, and F:

1. A > B ≥ C
2. C > D
3. E ≤ B
4. F < D
5. E > F

Which of the following conclusions is definitely TRUE?

Accepted Answer

Step 1: Establish the chain from constraints 1 and 2: A > B ≥ C > D Step 2: From constraint 4, F < D. Step 3: From constraint 5, E > F. Step 4: From constraint 3, E ≤ B. Step 5: Combine all chains: A > B ≥ C > D > F and E > F and E ≤ B Step 6: Test each conclusion: - Option A (A > D): From A > B ≥ C > D, we have A > D. TRUE. - Option B (E > D): E ≤ B and B ≥ C > D, so E could equal B or be less. If E = B and B = C, then E = C > D. But E could also be less than C. E > F and F < D, but this doesn't guarantee E > D. For example: A=10, B=8, C=7, D=5, E=6, F=4. Here E=6 > D=5. But try: A=10, B=8, C=7, D=5, E=5, F=4. Here E=5 = D. INDETERMINATE. - Option C (F > C): F < D and D < C, so F < C. This contradicts F > C. FALSE. - Option D (E = F): E > F from constraint 5, so E ≠ F. FALSE. Therefore, answer is A.

RRB Group D Statement & Assumptions

Statement & Assumptions— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Statement & Assumptions — Practice Questions

60-Second Revision — Statement & Assumptions